Analysis on manifolds is a broad area of mathematics that arose historically in the nineteenth and twentieth centuries from the study of physical problems. It relates to questions such as the shape of a soap bubble, the overtones of a drum, and even to basic questions in number theory, such as the distribution of primes. The gravitational force is described with great success by Einstein's theory of General Relativity, and the theory of the recently discovered Higgs boson also depends on the study of differential equations on manifolds. This Research Training Group project aims to increase the number of US students interested in pursuing the study of analysis, and more specifically, analysis on manifolds.
This grant will support a rich educational environment, for undergraduates, graduate students, and postdoctoral fellows in the field of analysis on manifolds, mentored by junior and senior faculty in the area. We will establish a summer workshop for advanced undergraduates and students at the threshold of graduate study, to increase their fluency in the language of modern analysis. We will enhance the courses in analysis available to our undergraduate students, and expand the range of research experiences for undergraduates. We will also conduct outreach activities among high school students and teachers in the Chicago region. The larger goal is to increase the number of well-prepared US citizens who pursue careers in the mathematical sciences, with a particular effort to increase the numbers of under-represented minorities in this field.